Entanglement with restricted measurement setups
Sebastian Meznaric · arXiv (Cornell University) · 2010
We consider what is the effective amount of entanglement when the measurement operators one has at their disposal are restricted. Such a scenario occurs when superselection rules are in effect or when there are imperfections in our measurement setup. Given a quantum state and the restrictions on measurements, we consider the following scenario. Imagine we have an ideal, or non-restricted, measurement setup and a state $\rho_1$ and a non-ideal, or restricted, measurement setup and a state $\rho_2$. Then the minimum amount of entanglement in $\rho_1$ so that all quantum communication protocols still perform with the same fidelity as with $\rho_2$ is effectively the entanglement with restricted measurement setup. For indistinguishable particles, we find that any quantum communication protocol that can be performed with indistinguishable particles, can thus be performed with a ``normal'' state of no more than $E_P$ of entanglement. For the imperfect measurement apparatus we find an upper bound for the effective entanglement, which is a linear function of the usual entanglement, with the proportionality factor dependent only on the imperfections in the measurement device.